There are a few mathematical concepts that can be quite useful in evaluating life situations or options, yet are simple to explain and can be applied without any number crunching or Math classes. Usually approximate answers will do. The usual use for philosophical math is to compare the answer for a given scenario against the answer for an alternative scenario to see which is the better choice. If the two answers are far enough apart to give a clear answer after accounting for margins of error, then it is obvious which is the better option.

First, a vector is simply something with magnitude and direction. It is usually symbolized by a line with an arrowhead at one end. The longer the line, the greater the magnitude. This idea of a vector is useful because it can represent a purpose.

Purposes also have magnitude and direction. Usually the direction is taken with reference to the pro-life purpose. (See earlier blogs for how to find the pro-life direction). The magnitude would be the strength of the purpose, which is a function of how strongly the individual feels about it or supports it. The direction, of course, would show how far off or how close to the pro-life purpose (or another purpose used as a reference) the given purpose is.

Use a diagram (which can often be “drawn up” mentally) to get an idea of how valuable a given purpose is. The value is determined by how long of a “shadow” the given purpose vector would project onto the reference purpose vector (which would usually be the pro-life purpose vector). The projection is done by drawing lines from the ends of the purpose vector to be projected to the reference purpose vector in a direction perpendicular to the reference vector. The longer the shadow, the more valuable the given purpose being evaluated. Remember to take into account the direction-indicating arrowhead of the shadow. If it points in the same direction as the pro-life purpose vector all is well and good. If it is pointing in the opposite direction to the pro-life purpose vector then you have gotten ahold of a bad one. The length of the projected shadow will determine how bad or good it is. For those of you interested in tying this in with more formal mathematics, the concept just described is called the “dot product” or “inside product” of two vectors.

Note that vectors are like butterflies— they are free! You can move them anywhere you like as long as you retain the direction and magnitude. This leaves you free to place them near one another in making specific comparisons.

The next concept of philosophical math is called “area under the curve”. It is another way to compare two or more alternatives to see which is best.

First I need to define pleasure as movement or advancement in the direction of the pro-life purpose. Now, make a graph of pleasure versus time, with the amount of pleasure shown as the distance in the direction of the Y-axis or vertical axis, and the amount of time shown in the direction of the X-axis or horizontal, and to the right from the starting point. The total amount of pleasure, then, is the area beneath the “pleasure curve”, to the right of the starting point in time, to the left of the ending point in time, and above the X-axis or “zero pleasure “ line. You can usually approximate the areas under two curves well enough to compare them-- but if not ask a calculus student to show you how, because finding the area under the curve is an important area of calculus called “integration”. You don’t really need to know calculus. You could always write a computer program (or use pencil and paper) to approximate the answer by breaking up the area into little rectangles having lengths equal to the height of the curve at a given point and small widths. How small? That is up to you. The smaller the widths, the closer the approximation, but the longer it will take to calculate. You just find the area of each of the small rectangles, which of course is just length times width, and add them all up. In most cases, though, an absolute value for the area is not needed. It is enough just to know which of two or more options has the greater area under the curve, and that can often be readily seen without resorting to any kind of calculation.

## Saturday, December 31, 2011

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